Sharp affine Trudinger–Moser inequalities: A new argument

We set up the sharp Trudinger–Moser inequality under arbitrary norms. Using this result and the $L_{p}$ Busemann-Petty centroid inequality, we will provide a new proof to the sharp affine Trudinger–Moser inequalities without using the well-known affine Pólya–Szegö inequality.

Social Conventions and Boundary Work in an Online Q&A: The Example of Vegetarianism and Veganism

The aim of this article is to explore the regulation of social conventions (more or less arbitrary norms of how one ought to act that are based on joint commitments) in online interaction. As the empirical case, the article scrutinises discussions about what it means to exercise vegetarianism or veganism. Drawing on ‘naturally occurring’ data from the question-and-answer platform Yahoo! Answers, conventions of vegetarianism and veganism are argued to be protected and upheld through symbolic boundaries, primarily in three forms: incompatibility, inauthenticity and noncommitment. Moreover, by utilising the platform’s system of thumbs-up and thumbs-down, it is argued that we are provided evidence of social approvals and sanctions in real time. The findings are suggested to have implications for continued theorising on conventions, studies of boundaries in the social sciences and analyses of social media as an arena for re-orientations of established sociological problems.

THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES

We study the classical Rosenthal–Szasz inequality for a plane whose geometry is determined by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case where the unit circle of the norm is given by a Radon curve, we obtain an inequality which is completely analogous to the Euclidean case. For arbitrary norms we obtain an upper bound for the perimeter calculated in the anti-norm, yielding an analogous characterisation of all curves of constant width. To derive these results, we use methods from the differential geometry of curves in normed planes.